Passive, proportional measurement of oxygen and carbon dioxide consumption for assessment of metabolic parameters

ABSTRACT

A conventional flow tube for a metabolic cart is usually a straight length of pipe whose inner diameter is fixed by the respiratory burden imposed by the flow tube on the user, with a smaller diameter imposing a higher respiratory burden. The ratio of the straight flow tube&#39;s length to diameter is fixed by fluid dynamics, so increasing the flow tube&#39;s diameter causes the flow tube&#39;s length to increase. As the flow tube gets longer, it exerts more torque on the user&#39;s neck and jaw, creating discomfort. Reducing the flow tube&#39;s length causes an undesired increase in the respiratory burden but increasing the flow tube&#39;s diameter to reduce the respiratory burden makes the flow tube less comfortable, making the flow tube unconformable, hard to breathe through, or both. Bending the flow tube, e.g., in an L shape, makes it possible to increase the flow tube&#39;s propagation length without increasing the flow tube&#39;s lever arm length.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the priority benefit, under 35 U.S.C. 119(e), ofU.S. Application No. 62/672,443, filed May 16, 2018, and entitled “ASystem for Passive, Proportional Measurement of Oxygen and CarbonDioxide Consumption for Assessment of Metabolic Parameters,” which isincorporated by reference herein in its entirety.

This application is related to concurrently filed U.S. application Ser.No. ______ (Attorney Docket No. MIT-19549US01), entitled “Methods andApparatus for Passive, Proportional, Valveless Gas Sampling andDelivery,” which claims the priority benefit, under 35 U.S.C. 119(e), ofU.S. Application No. 62/672,440, filed May 16, 2018, and entitled“Methods and Apparatus for Passive, Proportional, Valveless Gas Samplingand Delivery.” Each of these applications is incorporated by referenceherein in its entirety.

GOVERNMENT SUPPORT

This invention was made with Government support under Grant No.FA8702-15-D-0001 awarded by the U.S. Air Force. The Government hascertain rights in the invention.

BACKGROUND

Indirect calorimetry is a well-established methodology by which in vivogas exchange measurements, volume of oxygen consumed (VO₂), and volumeof carbon dioxide (VCO₂) exhaled by an individual are used to estimatethe rate of substrate utilization and energy metabolism (expenditure).Metabolic energy expenditure by an individual performing a specificactivity results in heat production and may also result in usefulmechanical work (e.g., when lifting a mass against the force of gravityfrom a given height to a greater height). Metabolic energy expenditureduring a given activity can be accurately estimated from VO₂ and therespiratory exchange ratio (RER) (i.e., the ratio of VCO₂ to VO₂). TheRER reflects the macronutrients being oxidized (predominantlycarbohydrates and/or fats). The RER, along with the volume rate ofoxygen consumed, allows estimation of the energy expenditure and themacronutrients (fuel substrates) being oxidized to providing metabolicenergy. The volume rates of oxygen consumption and carbon dioxideproduction can be determined non-invasively by constituent gas andvolume flow rate analysis of exhaled breath.

The science of indirect calorimetry was introduced over 100 years agoand exploits the stoichiometry of metabolic chemical reactions todetermine which and how many of the reactions are occurring. At the turnof the 20^(th) century, state of the art measurements required a trainedphysiologist to carry a large receptacle, typically a leak-proof bag,and stand or travel alongside a subject to collect exhaled breath andrecord the elapsed time for the breath collection. Following thecollection, the breath is analyzed to determine both the gas volumeexhaled per unit time and the oxygen and carbon dioxide concentrations.These measurements are combined to quantify (calculate) the subject'saverage energy expenditure during the period(s) over which the breathsamples were collected. This process is called the Douglas bag techniqueafter its inventor, Gordon Douglas, and is still used as a goldstandard.

Today, applications of indirect calorimetry generally fall into one ofthree architectural classes: whole room, mixing chamber, andbreath-by-breath devices. Each of these systems is designed to address aunique experimental need, resulting in different constraints,performance, and costs. Indirect calorimetry is typically used todetermine the energy expenditure associated with different physicalactivities (rest to vigorous activity) and/or the macronutrientsoxidized to provide providing metabolic energy during those activities.

The largest and most costly indirect calorimetry system is the wholeroom calorimeter. In this approach, the participant is confined to acontrolled space, typically a small ‘room’ just large enough for thecalorimetry equipment and with precise monitoring of the incoming andoutgoing gas composition and volume rate. Highly sensitive massspectrometers are used to measure the small changes in the gascomposition entering and leaving the room as the participant performsvarious activities as directed. The principle advantage of this approachis allowing metabolic fuel measurements to be made under relativelyunconstrained free-living conditions, where the participant is nottethered to a machine or required to breathe directly into a face maskor mouthpiece, all of which can limit or impact performance ofactivities. Whole room calorimeters are suitable for conductinglong-duration experiments, extending over days or weeks, and collectingdata over a variety of activities from sleep to high intensity exercise.

However, there are limitations to the types of activities that can beconducted in a closed room system, such as a whole room calorimeter. Forinvestigations of acute athletic performance or situational energyexpenditure during specified activities, other approaches are bettersuited. Another disadvantage of a whole room calorimeter is coarsetemporal resolution. A single exhaled breath may have a volume of aliter, whereas a whole room calorimeter designed to support a range ofactivities may have a volume of 20,000 liters or more. As a consequence,the time for exhaled breath to diffuse into the room and impact the gasconcentration as the air exits the room may be many minutes or hours,depending on the size of the room.

A second class of metabolic fuel sensor, the mixing chamber, oftenreferred to as a metabolic cart, evolved from the Douglas bag approach.Mixing chamber approaches have become the standard for laboratory andclinical measurements because they achieve relatively high temporalresolution and accuracy at much lower cost and ease of use thanwhole-room indirect calorimetry. In the mixing chamber approach,participants breathe directly into a facemask or specially designedmouthpiece equipped with a set of one-way check valves to control thegas flow direction and ensure that only the exhaled breath is collectedfor subsequent analysis. Unlike the sealed Douglas bag, the mixingchamber design allows a portion of the expired breath contained in themixing chamber to be ejected from the rear of the chamber in response toeach new breath. However, before a given breath is pushed out of themixing chamber by subsequent breaths, it passes through a series ofbaffles that mix each incoming breath with the residual from previousbreaths, forming an analog volumetric average of the previous fewexhaled breaths. Therefore, the exhaled breath mixture in the chamber atany time is a composite of a number of previous breaths and represents amoving metabolic average. Since the chamber is only large enough to holda few complete breaths, the temporal resolution is much higher than awhole room calorimeter.

FIG. 1A is a schematic of a unidirectional check valve assembly 100. Itshows the flow path to allow ambient air to flow into the user'srespiratory system from while diverting exhaled air via a third port 106to a mixing chamber (not shown). The unidirectional check valve assembly100 includes a unidirectional, normally-closed intake check valve 102that opens on inhalation to allow ambient air into the “T” on its pathto the user via port 104. While this intake valve 102 is open, an exitcheck valve 106 is closed. At the completion of the inhale cycle, therespiratory flow reverses direction, opening the exit check valve 106,which directs the bolus of exhaled gas into the measurement instrumentwhile the intake check valve 102 is closed. After the exhaled breath hasbeen transferred to the measurement device, the user inhales, reversingthe flow direction and again opening intake input check valve 102 andrepeating the cycle. The check valves 102 and 106 allow inhalation ofambient air and capture of exhaled breath for analysis while preventingthe incursion of ambient air into the measurement device and preventingloss of exhaled breath to the atmosphere during the breathing cycle.These valves 102 and 106, however, represent a respiratory burden to theuser and require finite amounts of pressure to open. The volume of the Tconnector also acts as a reservoir for a portion of the end tidalexhalation, which effectively increases the respiratory system's deadspace and results in a bolus of unanalyzed breath.

FIG. 1B shows how the check valve assembly 100 of FIG. 1A is connectedto a breathing tube 156 and a mixing chamber 160 for a typical metaboliccart. (The check valve assembly in FIG. 1B is flipped about the stem ofthe “T” with respect to FIG. 1A.) The user breathes out into the checkvalve assembly 100 via a mouthpiece 152. After the air exits the checkvalve assembly 100 via the exhale check valve 106 (FIG. 1A), it enters aconduit (breathing tube 156) that transfers the exhaled breath to thegas mixing chamber 160 of the metabolic cart. The breathing tube 156 isconnective plumbing between the user and the instrument. A flow meter158 at the entrance to the mixing chamber 160 measures the total volumeof the breath. Once the gas enters the mixing chamber 160, it is allowedto mix with previous breaths to form a volumetric average of the lastfew breathing cycles, before exiting the port at the back of the mixingchamber. It is the averaged breath in this chamber 160 that is sampledby a constant rate pump and delivered to O2 and CO2 gas analysis sensorsin an analysis chamber 164 coupled to the mixing chamber 160 via adrying line 162. Inside the analysis chamber 164, the gas constituentsare determined and associated with the measured flow data to provide theVO₂ and VCO₂ values used to computing the desired metabolic information.

For metabolic carts, the mixing chamber is a key component and servestwo purposes; first, it is of sufficient volume to capture and mixmultiple breaths to provide a running metabolic average, and second, itholds and isolates the collected breath from the environment, allowingit to be sampled and analyzed in a controlled fashion. The continuoussampling of gas from the mixing chamber and the displacement of gas witheach new exhale differentiates the modern metabolic cart from itshistorical Douglas bag predecessor, which held all of the exhaled breathin a sealed bag, to be analyzed after collection and thus provided onlyaverage values over the time of collection. In addition to gasconcentration measurements, calculation of energy expenditure requiresthe volume of the exhaled gas. The combination of the measured exhaledvolume, the inhaled gas composition (ambient air), and exhaled gasconcentration provide all the information needed for indirectcalorimetry calculations.

While much smaller and less costly than whole room calorimeters, theoverall weight and volume of metabolic cart systems makes themimpractical for ad libitum measurements and field studies. Specifically,a metabolic cart mixing chamber has a typical volume of 3-4 L. Withsupporting gas sensors, flow sensor, processor, and display, the systemvolume reaches more than 6 L and total weight increases enough to makethe system impractical for mobile use. Consequently, subject testingwith metabolic carts is typically conducted by trained operator andconstrained to a treadmill, stationary bicycle, or rowing machine in aclinical setting or laboratory environment.

The standard approach to create mobile systems for use in arbitraryenvironments is the so-called breath-by-breath method. To achieve thesmall size necessary for mobile use, breath-by-breath systems operate ona different principle than the previously described metabolic carts andwhole room calorimeters. These systems employ an “on the fly”measurement technique to avoid the requirement for a large mixingchamber capable of capturing and holding several breaths formeasurement. To eliminate the mixing chamber, breath-by-breath systemstypically make measurements of flow rates and gas concentrations every10-20 milliseconds (ms).

Rapid measurement of gas and volume allows the software to effectivelycarve up each breath into differential volume elements of about 10 to 20ms in duration. The volume rate of each breath sample is typicallymeasured at 50 Hz to 100 Hz by a spirometer near the mouth, while a pumpcontinuously removes a small percentage of the gas from the inhale andexhale stream at a constant pump rate independent of the instantaneousflow rate of the exhale or inhale breath. Once pumped, the gas sample ispassed through a flexible tube to fast-acting, series-connected O2 andCO2 gas concentration sensors. The sequential, rapidly measured gasconcentrations are then temporally aligned with the volumetric flowmeasurements to form the differential volume elements of O2 and CO2 foreach time interval. The differential volume elements are integratedtogether to produce a breath profile with a high temporal resolution,hence the name breath-by-breath system.

FIG. 2 shows a breath-by-breath collection device 200. In FIG. 2, thebreathing is conducted through a facemask 206 that measures the volumeflow rate of the breath by the spirometer exit port 202. Inside thebreathing mask 206, and before the spirometer 202, a pumping line 204removes a small continuous sample of gas and transports the sample to asensor suite 210. Inside the sensor suite 210, a pump 216 pulls thebreath through an oxygen sensor 212 and carbon dioxide sensor 214 anddeposits it back into the ambient environment.

For intra-breath dynamics and rapid metabolic changes, such as adjustingto a changing physical workload, breath-by-breath systems provide thehighest temporal resolution and mobility. Since the systems don'trequire a mixing chamber, they can be made sufficient small to bedirectly mounted on the subject and powered by a battery to enablemobile measurements of running, rowing, cycling, or energy demands of avariety of athletic and work-related activities.

However, a major challenge for breath-by-breath systems is ensuringaccurate time alignment between the flow and gas measurements when eachsensor is physically located in a different place and may exhibitdifferent measurement time constants. The alignment of all of thesesignals is sensitive to the arrangement of the device on the individual,the pump speed, calibration procedure, and the time constants andstructure of the individual sensors.

SUMMARY

Inventive calorimeters are small, inexpensive, and simple to use. Whenan expired gas flow is applied to one side of an inventive calorimeter,a fraction of the flow that is proportional to the instantaneous flowrate of the exhalation is diverted and passed to an exterior measurementchamber before cycling back and joining the main flow path. Unlike othercalorimeters, inventive calorimeters perform this flow-rate-proportionalsampling without valves or other moving parts. As gas flow is applied inthe other (inhale) direction, a fluid dynamic stall is developed acrossthe same gas sampling ports, effectively shutting off flow to themeasurement chamber, thus avoiding dilution of the exhale sample byambient air. This device can be used to collect a representative sampleof respired breath with little to no inclusion of diluting ambient gas.

An example of an inventive calorimeter is a flow-rate proportionalpassive side-stream sampling system with a bent flow tube, a mixingchamber, and at least one sensor. In operation, the bent flow tubereceives an exhaled breath from a person. The mixing chamber, which isin fluid communication with a first port between an inlet of the bentflow tube and an outlet of the bent flow tube, receives a fraction ofthe exhaled breath collected in proportion to an instantaneous flow rateof the exhaled breath. And the sensor, which is in fluid communicationwith gas in the mixing chamber, measures at least one of a volumetricflow rate, an oxygen content, a carbon dioxide content, an oxygenpartial pressure, or a carbon dioxide partial pressure of the fractionof the exhaled breath.

The bent flow tube may have a curve of about 75 degrees to about 105degrees between the inlet and the outlet. It may define an inner lumenextending from the proximal end to the distal end to convey the exhaledbreath from the proximal end to the distal end, with the first portbeing disposed between the bend and the outlet. The bent flow tube canhave a second port disposed between the inlet and the bend. It may alsohave: at least one valve, disposed between the inlet and the bend and influid communication with the inner lumen, to relieve pressure in theinner lumen during an inhalation by the person; a saliva trap, disposedin fluid communication with the inner lumen, to collect saliva excretedby the person; and/or a removable mouthpiece connected to the inlet ofthe bent flow tube.

The mixing chamber may include a perforated baffle and/or a perforatedcircuit board disposed between the inlet and the at least one sensor tofoster mixing of multiple breath fractions. The sensor can be disposedin the mixing chamber.

Another inventive aspect is a flow tube for a metabolic cart. This flowtube has a proximal end to receive an exhalation from a person, a distalend, and a bend between the proximal end and the distal end. It definesan inner lumen extending from the proximal end to the distal end toconvey the exhalation from the proximal end to the distal end. It has afirst port between the proximal end and the bend and a second portbetween the bend and the distal end to convey a portion of theexhalation to a mixing chamber in fluid communication with the lumen.The bend can be about 75 degrees to about 105 degrees (e.g., about 90degrees).

The flow tube may also have: at least one valve, disposed between theproximal end and the bend and in fluid communication with the lumen, torelieve pressure in the lumen during an inhalation by the person; asaliva trap, disposed in fluid communication with the lumen, to trapsaliva excreted by the person; and/or a removable mouthpiece insertedinto the proximal end.

All combinations of the foregoing concepts and additional conceptsdiscussed in greater detail below (provided such concepts are notmutually inconsistent) are part of the inventive subject matterdisclosed herein. In particular, all combinations of claimed subjectmatter appearing at the end of this disclosure are part of the inventivesubject matter disclosed herein. The terminology used herein that alsomay appear in any disclosure incorporated by reference should beaccorded a meaning most consistent with the particular conceptsdisclosed herein.

DESCRIPTIONS OF THE DRAWINGS

The skilled artisan will understand that the drawings primarily are forillustrative purposes and are not intended to limit the scope of theinventive subject matter described herein. The drawings are notnecessarily to scale; in some instances, various aspects of theinventive subject matter disclosed herein may be shown exaggerated orenlarged in the drawings to facilitate an understanding of differentfeatures. In the drawings, like reference characters generally refer tolike features (e.g., functionally similar and/or structurally similarelements).

FIG. 1A shows a schematic of a unidirectional mouthpiece.

FIG. 1B shows a schematic of a metabolic cart.

FIG. 2 shows a breath-by-breath indirect calorimeter.

FIGS. 3A and 3B show an inventive flow tube, also called a flow diode,that samples exhalation (FIG. 3A) but not inhalation (FIG. 3B).

FIGS. 3C and 3D illustrate how pressure differentials during exhalation(FIG. 3C) and inhalation (FIG. 3D) in a flow tube can be used topassively, proportionally sample a person's breath with a valvelessmixing chamber in a closed-loop metabolic collection system. The systemis illustrated as a straight flow tube with a delivery and return portplaced at locations to deliver gas to the sample/mixing chamber duringexhalation and to collect little to no gas during inhalation.

FIGS. 3E and 3F shows the flow tube of FIGS. 3A and 3B with the inhaleand exhale ports reversed.

FIG. 4A is a view of first side of a high-flow, bent/curved flow tubefor a closed-loop sampling system.

FIG. 4B is a perspective view of the bent flow tube of FIG. 4A.

FIG. 4C is a view of a second side of the bent flow tube of FIG. 1A.

FIG. 4D is a view of a third side of the bent flow tube of FIG. 1A.

FIG. 4E is a top view of the bent flow tube of FIG. 1A.

FIG. 4F is a bottom view of the bent flow tube of FIG. 1A.

FIG. 4G is a cutaway view of the mouthpiece of the bent flow tube ofFIG. 1A.

FIG. 4H is another perspective view of the bent flow tube of FIG. 1A.

FIG. 4I a cutaway profile view of a bent flow tube similar to the oneshown in FIG. 4A. It lacks a return port and is therefore suitable foruse with a valved mixing chamber.

FIG. 4J is a perspective view of a bent, low-flow flow tube for aclosed-loop sampling system.

FIGS. 4K and 4L show side views of a bent flow tube attached to a salivatrap and tubing that connects to a mixing chamber. Exhaled air passesunidirectionally out of the device, and some amount of flow occursduring inhale due to the cracking pressure of the valves.

FIG. 4M is a photograph of a bent flow tube with a scuba-stylemouthpiece, valves, and a saliva trap.

FIG. 4N is a photograph of a bent flow tube inserted into a Hans Rudolphvalve.

FIG. 5A is a schematic diagram of an active, breath-by-breathproportional sampling system.

FIG. 5B is a photograph of a passive proportional sampling system thatperforms like the one in FIG. 5A, but without an active valve on themixing chamber. This system behaves like the one shown in FIG. 5A butdoes not need an actively controlled pump.

FIG. 5C shows a mixing (measurement) chamber suitable for use in theproportional sampling systems of FIG. 5B.

FIG. 5D is a schematic diagram of an open-loop sampling system with abent flow tube and a valved mixing chamber. A pressure-creatingobstruction 503 paired with a check valve 530 acts as the pump shown inFIG. 5A.

FIG. 5E is a schematic diagram of a closed-loop sampling system with abent flow tube and a valveless mixing chamber.

FIG. 5F is a photograph of a woman wearing a closed-loop sampling systemwith a bent flow tube attached to a valveless mixing chamber as in FIG.5E.

FIG. 6 shows two breath exhale cycles and identifies the epochscomprising a typical breath cycle as well as the parameters of interest.

FIGS. 7A and 7B are bar charts showing the gas collection differentialvolume elements (DVEs) for constant rate versus proportional pumpingmethods.

FIG. 8 shows the velocity fields and pressure generated for a nearlydissipation-free flow around a 90-degree bend, e.g., as in the flow tubeof FIGS. 3A and 3B.

FIG. 9 shows the velocity fields and pressure generated for a nearlydissipation-free flow through a restriction.

FIG. 10A shows a diagram of an orifice plate placed in a horizontalfluid flow from left to right through a conduit or lumen.

FIG. 10B is a more detailed plot of the pressure change through anorifice plate.

FIG. 11 is a plot of pressure lost for a cone-shaped diffuser as afunction of the diffuser cone divergence angle. There is a minimum inpressure loss at a cone divergence angle of around 9 or 10 degrees, andthe pressure loss is greater on either side of the inflection point.

FIG. 12 shows the different levels of stall in flow through a diffuser.These flow patterns are responsible for variations in pressure recovery.

FIG. 13 is a plot of diffuser angle versus normalized length for conicaldiffusers (e.g., as in the flow tube of FIGS. 3A and 3B) andtwo-dimensional diffusers.

FIG. 14 is a plot showing the stability of the discharge coefficient fornozzles of differing geometries.

FIG. 15 is a plot showing the pressure recovery from the minimumpressure point in for flow through an orifice.

FIGS. 16A and 16B shows SolidWorks simulations of the pressure andvelocity fields inside of an asymmetric constriction geometry for flowin opposite directions (down in FIG. 16A and up in FIG. 16B).

FIG. 17 is a plot of the measured gas flow rate as a function ofpressure differential across the flow tube for a generic sensor.

FIGS. 18A and 18B shows a secondary method of reducing the amount offlow into the auxiliary chamber when the flow tube is used as acollection device.

FIG. 18C shows a design for a Tesla flow diode which uses the principleillustrated in FIGS. 18A and 18B to create mono-directional flow.

FIG. 19 is a plot showing the effectiveness of the passive proportionalvalveless sampling technique for three different high-flow flow tubeslike the one in FIGS. 3A and 3B.

FIG. 20 shows the same data set as FIG. 19, but for a flow tube like theone in FIGS. 3A and 3B with a higher respiratory burden.

FIG. 21 shows the raw data used to estimate or determine the volume ofexhale/inhale entering the collection chamber in the passive side streamsampling system of FIG. 5B. It shows that the flow rate of gas enteringthe chamber varies over many breathing cycles, starting from rapid flowat the beginning to slower flow by the end.

FIG. 22 is a close-up of a few breathing cycles from FIG. 21.

FIG. 23A is a cross-sectional view of the mixing chamber illustrating aperforated baffle and perforated circuit board disposed therein, whichaid in mixing the expired boluses of gas before same arrive at the atsensor(s).

FIG. 23B is a top, cut-away view of the mixing chamber and perforatedcircuit board shown in FIG. 23A.

DETAILED DESCRIPTION

Inventive embodiments include a low-cost sensor that combines featuresfrom the breath-by-breath and metabolic carts. This sensor uses aninnovative passive proportional side-stream gas collection mechanism toextract a small fraction from the exhale flow with an extraction ratethat is directly proportional to the exhale flow rate. Thisproportionality remains stable or constant over the entire exhalation,regardless of the flow rate or pressure—for instance, the passiveproportional side-stream gas collection mechanism may extract 1% of theexhaled breath over the entire pressure/flow rate range of the exhaledbreath. This percentage or proportion may vary slightly with respirationrate or barometric pressure and falls to zero when the gas flows in thereverse direction (i.e., when the subject inhales).

By diverting a small proportional sample from the main flow stream,rather than collecting the entire breath, the mixing chamber used tocontain the breath sample is drastically reduced in size, from severalliters to a fraction of a liter. However, by capturing a proportionalsample of the breath, the fidelity of exhale breath gas concentrationsis preserved: when converted to standard temperature and pressure (STP)conditions, the volume concentrations of gases in each exhaled breathfraction in the mixing chamber is the same as the volume concentrationsof gases in the corresponding entire exhaled breath. As a result,sensors in the mixing chamber or coupled to the output of the mixingchamber can measure the gas properties and, if they're in the mixingchamber, act as flow mixing obstacles.

The exact percentage of exhaled breath siphoned out of the exhale flowmay be set based on the size of a mixing chamber used to capture andaverage the exhaled breath fractions. The percentage may range fromabout 0.5% to about 2.5%, depending on the application and the size ofthe mixing chamber. For example, with a 1% proportionality, a nominal3-liter mixing chamber can be shrunk by a factor of 100 to 30 mL. (Atradeoff between percentage and mixing chamber size is that smallerproportional samples fill the chamber more slowly.) For restingmetabolic measurements, the percentage may be larger (e.g., more than2%) to improve measurement fidelity; for making metabolic measurementsduring exercise, the percentage may be smaller (e.g., less than 1%) toreduce the respiratory burden. Smaller percentages may be possible forsmaller mixing chambers or for more sensitive sensors, such aselectro-chemical sensors.

The size of the mixing chamber varies with the percentage of extrabreath siphoned out of the exhale flow, the number of breaths beingaveraged, and the speed of the sensors used to measure the gasconcentrations. In general, the mixing chamber should be large enough tohold the volume equivalent of one full breath (also called the breathequivalent volume (BEV)) at a minimum and up to 5 to 10 BEVs. The mixingchamber can be larger, e.g., for capturing portions of a substantialnumber of breaths (say, 100 breaths or more) for longer averaging times(slower sensors), for eliminating confounds due to short perturbationsin breathing, or for resolving ventilation/perfusion (V/Q) mismatchfollowing postural changes.

The desired uncertainty of gas concentration measurements also affectsmixing chamber size. The uncertainty is a function of the number ofbreath equivalents within the mixing chamber—the more breaths in themixing chamber, the more accurate and repeatable the gas concentrationmeasurement. From the perspective of optimizing performance, the gasconcentration uncertainty should be comparable to the sensor uncertainty(and both should be as low as practically achievable). Other effectssuch as adsorption/desorption from internal surfaces are also important,but these should quickly stabilize during use.

The sensors can be fast (e.g., with response times of less than 500milliseconds) or slow (e.g., with response times of more than 1 second).One benefit of the passive, proportional sampling is the ability toprovide an extended dwell time with the proper gas mixture within themixing chamber, allowing the use of slower, less expensive, moreefficient, and often longer-lived gas sensors. In general, the gassensor should be fast enough to sample the maximum rate-of-change in thegas concentration within (or just following) the mixing chamber at orabove the Nyquist sampling rate, which is twice the maximumrate-of-change. The maximum rate-of-change is a function of thebreathing rate, breathing (tidal) volume, proportional sampling fractionof the gas splitter, and mixing chamber volume. At a minimum, thesampling rating would be once per breath.

As an example, consider a breathing rate of 10 breaths per minute (bpm)(5 liters per minute (lpm) total), a tidal volume of 500 cc, aproportional sampling fraction of 1% for a sample flow of 50 cc/min intothe mixing chamber, and a mixing chamber volume of 100 cc (abreath-equivalent volume (BEV) of 20). In this example, the gas exchangehalf-life is about 1 minute, because in 1 minute, the subject displaceshalf of the gas within that chamber (50% dilution). Assuming goodmixing, in the second minute, the subject displaces 75% (100%+50%, withthe sum divided by 2) of the gas within the mixing chamber.(Alternatively, think of this as a 20 BEV mixing chamber with a gasmixing time constant of 1 minute.)

The gas sensors can respond slowly, so long as the sensor output hasreached equilibrium with the actual gas concentrations being measuredbefore the measurement is interrupted (e.g., because the sensor isturned off). Typically, faster response is preferred. But a sensor thatresponds faster is usually more expensive than a slower sensor andsometimes also involves consumables. The ability to also use slowersensors in an inventive sampling system is therefore a big advantageover other metabolic measurement systems.

1 FLOW PROFILES AND PRESSURE IN A VALVELESS, PASSIVE, SIDE-STREAMSAMPLING SYSTEM

A valveless, proportional, passive system produces a flow profile thatcan be used to make metabolic measurements with a miniaturized mixingchamber. For metabolic measurements, the user simply breathes in and outthrough the short end of the flow tube into a valveless mixing chamber.Together, the flow tube and the valveless mixing chamber form a passive,proportional, closed-loop metabolic sampling system. As the breath isexhaled, it is compressed while traveling around a 90-degree bend into avena contracta at the start of the other leg, before expanding back tothe original cross-section in the exit diffuser. Upon inhale, the gastravels in the opposite direction, where it is compressed beforeexpanding around the bend back into the original diameter. The asymmetryin design creates conditions where a finite pressure difference betweenthe front of the flow tube, P_(A), and the vena contracta, P_(C), on anexhale forces air into the mixing chamber, and the null pressuredifference formed on inhale prevents ambient air from entering themixing chamber with no need for a mechanical valve or moving parts.

Without being bound by any particular theory, the asymmetry betweeninhale and exhale is a result of non-ideal fluid flow and differentdissipation processes for the two flow directions. For an ideal orconservative system, the pressure profile inside the flow tube would bethe same for either direction and depend only on the diameter andcurvature of the flow tube. For non-dissipative flow, the pressure fieldis defined by the Bernoulli effect,

$\begin{matrix}{{P_{1} + \frac{\rho \; V_{1}^{2}}{2} + {{gh}\; \rho}} = {{Constant}.}} & {{Equation}\mspace{14mu} 1}\end{matrix}$

Ignoring minor gravitational effects, the difference in pressure at anytwo locations is a direct result of the changing speed of the flow. Thevelocity and pressure drop through a constriction has the same generalform, A₁V₁=A₂V₂, where A₁ and A₂ are the cross sectional area atlocations 1 and 2 respectively. The pressure change can solved as

$\begin{matrix}{{\Delta \; P} = {\frac{\rho}{2}{{V_{1}^{2}( {1 + \frac{A_{1}^{2}}{A_{2}^{2}}} )}.}}} & {{Equation}\mspace{14mu} 2}\end{matrix}$

For dissipation free flow around a 90-degree bend, the velocity profilesare, xV_(x)=RV_(R), where x and R are defined in FIG. 8. The pressuredrop across the 45-degree line is

$\begin{matrix}{{\Delta \; P} = {\frac{D}{r}\rho \; {V^{2}.}}} & {{Equation}\mspace{14mu} 3}\end{matrix}$

These pressure changes are recoverable since, in the construct of theBernoulli equation, there is no loss mechanism. In real systems, thereare dissipative pressure loss events affecting the fluid flow. It is thedissipative effects that create the asymmetry in the flow tube.

The concept of dissipative vs. dynamic pressure change is shown in FIGS.10A and 10B for an orifice plate in a straight tube. In this example,there are three labeled pressure ports: a, b, and c, which correspond toP_(A), P_(C), and P_(B) in FIGS. 3A-3D, respectively. In this example,the fluid begins at some arbitrary pressure P_(a) and velocity V_(a) onthe left hand side before traveling through the constriction at locationb and expanding back to the original diameter at location c. As thefluid flows, the pressure and velocity will change to reflect theenvironment. The pressure decreases inside the constriction, with thereduction in pressure due to loss mechanisms, such as heat, andconversion into kinetic energy as predicted by Equation 3. After exitingthe constriction, the diameter of the tube increases to thepre-constriction diameter and roughly speaking the kinetic energy isconverted back into pressure. However, much like the path from a to b,some of the energy is lost to heat and P_(c) is lower than P_(a) for thedissipative system (second, third, and fifth bars counting from the leftof FIG. 10A). When the fluid flow is reversed and P_(c) is the startingpressure, P_(b) maintains its low pressure, but P_(a) is smaller thanP_(c), by the amount indicated by the curve in FIG. 10A. As a result,there is an asymmetry in the differential pressure between P_(a) andP_(b), depending on the flow direction. The ideal system with fullpressure recovery is shown by the first, fourth, and sixth bars countingfrom left in FIG. 10A.

The pressure recovery, or the ability of the system to return frompressure P_(b) to the original pressure (P_(a) for the left to rightdirection and P_(c) for the other) is a measure of the dissipation inthe system and is commonly reported as a discharge coefficient (C_(d)).A system with a high discharge coefficient will have a pressure profileresembling the green bars and a low discharge coefficient will be moresimilar to the red. For a system like the orifice geometry in FIGS. 10Aand 10B, locations for a and b and the constriction diameter could bechosen such that the forward flow (a→c) there is a large pressuredifference between the a and b locations, ΔP_(ab). It is this pressuredifference that is used to drive the gas into the chamber coupled to theflow tube in FIG. 3A. However, for the opposite flow direction (c→a) thedischarge coefficient and gas extraction points can be designed suchthat there is little or no pressure recovery between b and a, shown inFIG. 10B. This arrangement will create an effective flow diode, wherewithout the need of mechanical valves or pumps. Gas will flow into anauxiliary chamber during exhale and that same chamber will be stagnanton inhale. However, when designing a system for human interaction thereare additional concerns beyond proportional sampling and diode behaviorrelated to usability.

2 FLOW DIODES FOR VALVELESS, PASSIVE, SIDE-STREAM SAMPLING

FIGS. 3A and 3B show an inventive passive proportional sampling device,also called a flow tube 300, that samples exhalation (FIG. 3A) but notinhalation (FIG. 3B). The flow tube 300 samples a single direction of anAC gas flow passively, without any moving parts, relying on thedirection of flow imparted at the source. More specifically, FIGS. 3Aand 3B show a flow tube 300 that passively diverts a proportional amountof exhale into a mixing or measurement chamber (e.g., as shown in FIG.5C; inserted in between ports 304 and 306) while preventing flow intothe same chamber during inhale. The flow direction for inhale and exhaleis shown by arrows running along a central conduit or lumen 312 in theshape of a rotated “L” or “J.” FIG. 3A shows fluid entering through afirst port 302 at the top left, moving around the bend in the lumen 312,and exiting through a second port P_(B) the bottom. FIG. 3B shows theinhale, with fluid entering through the second port 308 and moving upthe flow tube 300 and out the first port 302.

The flow directions in FIGS. 3A and 3B create natural pressuregradients, which are shown by the shading. For the exhale in FIG. 3A,the shape of conduit (lumen 312) causes a large positive pressure todevelop at the top of the device, before reaching a minimum pressurearound port P_(C), before regaining some of the lost pressure before theexit at port P_(B). The inhale starts with a large negative pressure atthe human interface (mouthpiece) at the first port 302, but the gas flowstarts at the port P_(B). The gas loses pressure as the cross section ofthe conduit 312 decreases (indicated by reference numeral 310), untilthe minimum pressure is achieved near P_(C). However, with flow in thisdirection, pressure recovery is discouraged and does not increase backto ambient pressure.

The large pressure difference of about 300 Pa on the exhale flow patternis used to drive gas between intermediate ports P_(A) and P_(C). Sincethis pressure difference is generated by the flowing fluid, its absolutemagnitude is proportional to the flow rate of the fluid. Theproportionality in generation and usage is used to collect constantfractions of the total fluid flow. For flow in the other direction, verylittle pressure difference is generated between P_(A) and P_(C), so nogas is pushed between ports P_(A) and P_(C). This is represented in thefigure by large X's over the ports in FIG. 3B.

FIGS. 3C and 3D show an iteration of an inventive closed-loop samplingsystem with a symmetric flow tube 301 connected to a valveless mixingchamber 320 during a person's exhalation and inhalation, respectively.It also shows the pressures at ports P_(A), P_(B), and P_(C) duringexhalation and inhalation. As the person exhales, the pressure at portP_(A) is higher than the pressures at ports P_(B) and P_(C), as in thebent flow tube 300 in FIGS. 3A and 3B, causing a percentage of theperson's breath to flow into the mixing chamber 320, where oxygen andcarbon dioxide sensors 322, 324 measure its oxygen and carbon dioxidecontent, e.g., at a sampling rate of 0.2 Hz to 20 Hz. (The oxygen andcarbon dioxide sensors 322, 324 can also be located outside the mixingchamber 320, e.g., in or along the return tubing connecting the outputof the mixing chamber 320 to the flow tube 300.) As the person inhales,the pressure at port P_(A) drops below the pressure at port P_(C), whichremains lower than the pressures at port P_(B). This pressuredifferential prevents the gas being inhaled from flowing into the mixingchamber 320 via port P_(B).

FIGS. 3E and 3F shows the flow tube 300 of FIGS. 3A and 3B with theinhale and exhale ports reversed. Reversing the inhale and exhale portsmakes the flow tube suitable for proportionally removing and mixingmaterial from an auxiliary chamber (not shown) coupled to ports P_(A)and P_(C) into a single direction of flow path in an AC flow. In thisusage of the flow tube, the user exhales through the long straightportion, rather than the short bent portion as in FIGS. 3A and 3B. Inthis orientation the external chamber (not shown but located betweenports P_(A) and P_(C)) is an extraction chamber rather than a collectionchamber. The extraction chamber can be filled with emulsified liquid,saturated vapor, or an agitated and dispersed powder. This material isfiltered into the breathing port through P_(C) during inhale in ameasured way.

Much like the device in the breath collection mode, different pressureprofiles are developed for the different flow directions. In the exhaledirection (FIG. 3E), side-stream ports P_(A) and P_(C) have equalpressure, discouraging flow into or out of the extraction chamber. Thisrestricts the loss of the aerosolized material into the localenvironment. During an inhale, the pressure gradients should force aknown amount of the aerosolized material into the inhale flow stream andto the user. If the density of the aerosolized material in theextraction chamber is known, then the volume of fluid exiting theextraction chamber can be estimated or determined on a breath-by-breathbasis.

The ease, passivity, and unidirectional flow of this device allows theuser to comfortably inspire the inhalant over the course of manybreaths. Additionally, measuring the user's minute volume may enabledirect measurement of the inhalant dose. With these combined effects, alower dose density per breath could be used, easing the aerosol mixingrequirements on the inhalant.

3 A BENT OR CURVED FLOW TUBE FOR METABOLIC MEASUREMENT

The flow tube 300 shown in FIGS. 3A and 3B is bent, curved, angled,elbow-shaped, L-shaped, or J-shaped. This shape makes it easier tomeasure a person's metabolic rate in the field or in a laboratory. Thebent flow tube is more stable and comfortable to use due to thereduction in cantilevered mass. And the higher pressure at the outerradius of the bend in the inverted bent flow tube increases the flow tothe mixing chamber.

The bent flow tube has a removable, flexible, snorkel-like mouthpiecewith bite-wings for comfortable, hands-free use of the flow tube duringvigorous physical activities.

The flow tube also has an integrated, transparent saliva trap thatprevents the test subject's saliva from dripping out of the flow tubeand reduces the likelihood of saliva obstructing the tubes leading thedifferential pressure pneumotachometer and/or to the tubes leading to(and from) a mixing chamber. Repositioning the tubes leading to themixing chamber to the upper/distal surface of the bent flow tube alsoreduces the likelihood of the tubing becoming clogged by saliva.

The bend allows the flow tube to be both wide and long, thereby reducingthe torque exerted by the flow tube on the test subject's head and neckwithout unduly increasing the test subject's respiratory burden.Compared to current devices for measuring metabolic rate, a metaboliccart with a bent flow tube can be smaller, lighter, less expensive, moreefficient. In fact, a system with a bent flow tube can be completelypassive (i.e., without a pump). As a result, the entire system can becarried by or mounted on the person whose metabolic rate is beingmeasured. And because such a system is reliable and compact, it'spossible to use several of them at once (e.g., in a laboratory).

A bent flow tube has a number of advantages over straight flow tubes ofsimilar length. First, the bend reduces the lever arm length of the flowtube when the proximal end is inserted into a test subject's mouth. Thismakes wearing the flow tube more comfortable for the test subject. Italso simplifies the tubing connections between the flow tube and themixing chamber by eliminating 90-degree bends between the tubing andmouthpiece, e.g., as in FIG. 27 of US Pre-Grant Publication No.2017/0055875 A1. And it reduces visual obstructions for the test subjectand the effects of wind and movement on the metabolic measurementsbecause the distal end faces downward instead of outward.

FIGS. 4A-4J show different views of a high-flow, bent flow tube 100suitable for measuring a person's metabolic rate in the field or thelaboratory. The flow tube 100 comprises a length of tube with a bend 440between a proximal end 410, or mouthpiece, and a distal end 460.Depending on its curvature, the flow tube 100 may have a maximum innerdiameter of 1.1″, a minimum inner diameter of 0.32″, and a length of 8″.It could also have a maximum inner diameter of 1.1″, a minimum innerdiameter of 0.785″, and a length of 7.75″. Other dimensions are alsopossible. Similarly, the bend 140 in FIGS. 4A-4H is about 90 degrees,but bends of other angles (e.g., 75 degrees to 105 degrees) andorientations are also possible. For instance, the flow tube 400 couldpoint sideways or be curved (e.g., in a spiral).

The flow tube 400 defines a lumen 402 that extends from the proximal end410 to the distal end 460. The lumen's cross section varies along thelength of the flow tube 110 as shown in FIG. 4I. The flow tube 400 alsodefines several ports or openings between its outer surface and thelumen 402, including valve ports 120, a saliva trap connector 430, oneor more proportional sampling ports 450, an exit pressure port 452, andan exhale chamber port 454. And it has seats 470 for O-rings at thedistal end 460.

The length of the flow tube 400 extending from the bend 440 to thedistal end 460 is fixed by the shape of the inner lumen 402. The lumen'sdiameter is wider at the distal end 460 and the proximal end 410 andnarrow at or near the bend 440. The length of the flow tube 400 isusually chosen so that the slope from the lumen's smallest diameter(e.g., the flow constriction 442 shown in FIG. 4I) to its largestdiameter at the distal end 460 is about 9° to 10°. This slope isintended to maintain a low expiratory respiratory burden for the testsubject.

The portion of the flow tube 400 extending from the bend 440 to theproximal end 460 is long enough to fit the valve ports 420 and thesaliva trap port 430 between the proximal end 460 and the bend 440.Valves and a saliva trap (not shown) may be fitted to these ports. Thesaliva trap and saliva trap port 430 are positioned to prevent thesaliva tube from hitting the test subject's chest.

The valves that fit into the valve ports 420 address a technical problemthat affects bent flow tubes but not straight flow tubes. Although theJ-shape of the flow tube 400 allows for large diameter and longlength—and thus a low respiratory burden when exhaling—it increases therespiratory burden when inhaling. The valves near the mouthpiece 410address this problem by cracking open at low pressure when the testsubject inhales. The valves balance or equalize the respiratory burdenfor inhaling and exhaling. The valves remain close when the test subjectexhales, so they don't affect the metabolic measurement.

The saliva trap that fits into the saliva trap port 430 catches salivaexcreted by the individual that might otherwise corrupt or interferewith the metabolic measurement. For many test subjects, the mouthpiecetriggers salivation. Gravity siphons saliva from the test subject'smouth into the saliva trap via the saliva trap port 430 and a channel ordepression 412 (FIG. 4G) in the inner portion of the mouthpiece 410.This prevents the saliva from clogging tubes connected to the mixingchamber ports 450 and keeps the saliva away from clothing.

The mixing chamber ports 450 can be connected to a mixing chamber (FIG.5C) via respective selective, permeable tubing (FIGS. 4K and 4L).Suitable tubing includes Purma Pure Nafion™ tubing, which is composed ofsynthetic polymers capable of functioning under relatively hightemperatures (e.g., greater than 100° C.) acting as an efficientdesiccant of the breath sample, or other tubing composed of ionomersthat provide similar material properties to effectively dry the breathsample. If desired, the mixing chamber ports 150 and tubes may beconnected using secure Luer lock attachments to reduce the likelihood ofunintended tubing disconnections. As the test subject exhales, a portionof the exhaled gas passes through at least one of the mixing chamberports 450 and corresponding tube to the mixing chamber, where it can beanalyzed to determine the test subject's metabolic rate. The exhaled gasis dried as it passes from the flow tube through the Nafion™ tubing tothe mixing chamber where CO₂ and O₂ concentrations are measured. Dryingthe exhalant is advantageous to gas analysis at the mixing chamber. Theexhalant can also be dried with a heater (not shown).

The flow tube 400 can also be connected to a metabolic cart instead ofor in addition to the mixing chamber via its distal end 460. The distalend 460 has grooves 470 for O-rings to seal the connection or interfacewith a tube for the metabolic cart.

As mentioned above, FIGS. 4A-4H show a high-flow, bent-shaped flow tube400. It is designed for intense exercise, to support peak expiratoryflows of around 300 lpm without presenting an objectionable respiratoryburden. To support this peak expiratory flow rate, the high-flow,bent-shaped flow tube 400 has a diameter of 0.785″. At rest, however,with peak expiratory flows as low as 20-25 lpm, there is insufficientflow resistance (back pressure) to ensure a good sample of the breath.As a result, it works at low flows but just takes a really long time tofill the sample chamber.

FIG. 4J shows a low-flow, bent flow tube 490 designed to ensure goodsampling at resting expiratory flows (e.g., 20-25 lpm). It is similar inshape and size to the high-flow, bent flow tube 400 in FIGS. 4A-4H, buthas a narrower lumen diameter and is slightly longer. It can be used upto peak values of 80 lpm without saturation. Since the high-flow andlow-flow bent flow tubes have an overlapping range, one metabolicmeasurement protocol is to use the low-flow, bent flow tube 490 formeasuring the metabolic rate while the test subject is resting and ordoing low-intensity exercise, such as walking, in order to fill themixing chamber in reasonable time, and to switch to the high-flow, bentflow tube 400 for moderate to intense exercise.

FIGS. 4K and 4L show opposite sides of a bent flow complete with asaliva trap, valves, and tubing that connects to a mixing chamber (see,e.g., FIG. 5C). This tubing is connected to ports PA, PB, and PC asdescribed above. FIG. 4M is a photograph of a bent flow tube with ascuba-style mouthpiece, valves, and a saliva trap. And FIG. 4N shows abent flow tube whose distal end is connected into a commercialHans-Rudolph valve, which is what a ParvoMed metabolic cart uses for thesubject to breathe into. The skinny tube jutting out of the Hans Rudolphvalve is a separate spit trap. In this orientation, the innovativemetabolic device can produce concurrent measurements on the same breathdata.

4 A PASSIVE, PROPORTIONAL, CLOSED-LOOP SIDE-STREAM SAMPLING WITH A BENTFLOW TUBE AND VALVELESS MIXING CHAMBER

FIG. 5A is a schematic diagram of a proportional sampling system 580.Like the breath-by-breath system 200 shown in FIG. 2, the proportionalsampling system 500 in FIG. 5A includes a facemask 586 with a spirometer582 that measures the volume flow rate of the breath. Inside thebreathing mask 586, and before the spirometer 202, a pumping line 584removes a small continuous sample of gas and transports the sample to amixing chamber 590. Inside the mixing chamber 590, a pump 596 pulls thebreath through an oxygen sensor 592 and a carbon dioxide sensor 594 anddeposits it back into the ambient environment

One difference between the proportional sampling system 580 shown inFIG. 5A and the breath-by-breath system 200 shown in FIG. 2 is theaddition of a feedback signal between the pump 596 and the flowmeasurement device (spirometer 582). This feedback is representedconceptually by a wire 598 connecting the spirometer 582 and the pump596 in the FIG. 5A. The feedback signal adjusts the pumping speed of thepump 596 in response to the spirometer measurement. This additionalfeedback creates a proportional side stream system and avoids the needto rapidly measure and time align gas sample concentrations.Furthermore, the unidirectional nature of the pump 596 eliminates theneed for a mechanical valve on the mixing chamber 590 to preventdilution of the mixing chamber sample during the inhale breath cycle.

The gas exiting the face mask 586 through the exhale drying line 584 ismetered by the pump 596 and enters the mixing chamber 590 that housesthe sensors 592 and 594. (This is different than the system 200 of FIG.2, which pulls gas through each of the sensors at a continuous fixedflow rate independent of the breath flow rate.) After the gas enters themixing chamber 590, it mixes with the gas already present in the mixingchamber 590 before being pushed out by subsequent pump samples.

Proportional pumping enables the use of the mixing chamber 590, similarto the metabolic cart of FIG. 1B, to average several breaths at once.But the proportional sampling and mixing chamber 590 eliminate the timealignment between the gas sensing and flow sensing elements required bya metabolic cart. Furthermore, shutting off the pumping during inhaleavoids diluting the gas sample in the mixing chamber with ambient air.

FIG. 5B is a photograph of a passive proportional sampling system 570.It performs like the one in FIG. 5A but is completely passive and doesnot require the use of an active pump or a mechanical valve on themixing chamber. The flow tube 300 is the same one shown in FIGS. 3A and3B and has a bite grip 572 that fits into the intake port for the testsubject to stick in his or her mouth and a nose clip 574 to prevent thetest subject from breathing in or out through his or her nose. Thepressure differences naturally occurring in the flow tube 300 in FIG. 5Bact as the pump 596 and the feedback connection 598 in FIG. 5A. Theexhale drying line 540 in FIG. 5B is shown as the single-headed arrowsleaving the flow tube 300, and the exit port of the pump is representedby the single-headed arrows returning to the flow tube 300. Thedouble-headed arrows in FIG. 5B represent the flow traveling through thespirometer 582.

FIG. 5C shows side view (top) and a rear view (bottom) of the valvelessmixing chamber 512 for use in the proportional side-stream samplingsystem 570 of FIG. 5B. The mixing chamber 512 includes a cavity 511 thatreceives exhalations from a user via tubing connected to a flow tube(see, e.g., FIGS. 4K and 4L). This tubing may include a proportionalsampling tube that delivers a proportional amount of each exhalation tothe mixing chamber and a flow return tube that delivers a portion of themixing chamber's contents to the flow tube. These tubes are connected toports 513 and 516, respectively, in the rear of the mixing chamber.

The mixing chamber cavity 511 holds one or more sensors (collectively,sensors 520) that measure the volumetric flow rate, the oxygen content,the oxygen partial pressure, the carbon dioxide content, the carbondioxide partial pressure, etc. These sensors may include, but are notlimited to, an oxygen sensor 520 a and a carbon dioxide sensor 520 b. Italso has ports for high-pressure and low-pressure measurements in theexhale direction. The sensors can be mounted on an electronics board 522(e.g., a printed circuit board) and powered by batteries 524 or anothersuitable power supply as shown in FIG. 5C. The mixing chamber cavity 511is small in size (interior volume, which may be about 1 BEV to about 20BEVs (500 ccs to 10,000 ccs)) to allow rapid filling during rest andactivity as a factor of individual lung capacity.

FIG. 5D illustrates a closed-loop, passive, proportional side-streamsampling system 500 with the bent flow tube 400 of FIGS. 4A-4I and avalved mixing chamber 510 to prevent dilution of the gas samplecontained in the chamber during inhalation. The inlet of the bent flowtube 400 fits into the mouth of a person 501, possibly with a mouthpiecefor a better fit/seal. As the person breathes out, most of theexhalation 503 travels through the flow tube 400 to the outlet. Aconstriction 442 in the flow tube 400 creates a pressure gradient thatforces a proportional amount 505 of the exhalation out of the exhalepressure port 454. This proportional amount 505 travels through tubing540 to the mixing chamber 510.

The proportional amount 505 mixes with fractions of the user's earlierbreaths in the mixing chamber 510. At the same time, one or more sensors520 in the mixing chamber 510 measure the partial pressures of oxygen,carbon dioxide, etc. in the mixing chamber 510. When the pressure in themixing chamber 530 reaches a threshold, excess gas vents out of thevalved mixing chamber 510 via a check valve 530 that prevents gas fromentering the mixing chamber 510 when an individual 501 inhales.

FIG. 5E illustrates the open-loop, passive, proportional side-streamsampling system 570 of FIG. 5B with the bent flow tube 400 of FIGS.4A-4I and a valveless mixing chamber 512. Again, the inlet of the bentflow tube 400 fits into the mouth of a person 501, possibly with amouthpiece for a better fit/seal. As the person breathes out, most ofthe exhalation 503 travels through the flow tube 400 to the outlet. Aconstriction 442 in the flow tube 400 creates a pressure gradient thatforces a proportional amount 505 of the exhalation out of the exhalepressure port 454. This proportional amount 505 travels through tubing540 to the valveless mixing chamber 512.

Again, the proportional amount 505 mixes with fractions of the user'searlier breaths in the valveless mixing chamber 512. At the same time,one or more sensors 520 in the mixing chamber 512 measure the partialpressures of oxygen, carbon dioxide, etc. in the mixing chamber 512.Excess gas travels out of the mixing chamber 512 to the port P_(C) ofthe bent flow tube 400 via a return tubing 542. The sensors 520 can alsobe located in or in fluid communication with the return tubing 542instead of in the valveless mixing chamber 512. The sensors 520 can evenbe located at or just before port P_(C) of the bent flow tube 400.

FIG. 5F is a photograph of the open-loop, passive, proportionalside-stream sampling system 570 with the bent flow tube 400 in operationwith the valveless mixing chamber 512. A plastic tube in the testsubject's mouth fits over the proximal end of the flow tube. If desired,this plastic tube may be replaced with a scuba-style bite mouthpiece(e.g., bite grip 572 in FIG. 5B) fitted into the proximal end 410 asshown in FIG. 4M to create a better seal between the test subject'smouth and the flow tube 400 and to make the flow tube 410 morecomfortable for the test subject.

With proximal end 410 properly in place, the bend 440 causes the distalend 460 of the flow tube 400 to point down or at an angle. Because theflow tube 400 bends down, it doesn't extend as far out of the testsubject's mouth. Thus, compared to a straight flow tube with the samelength, the bent flow tube 400 has a shorter lever arm length, reducingthe torque that it exerts on the test subject's jaw, head, and neck.

5 RESPIRATORY BURDEN

Respiratory burden is a physiological measure of difficulty associatedwith the mechanics of breathing. This is a pressure difference betweenthe gas as it is exhaled by the subject and that of the ambientenvironment. In FIG. 10A, this is the difference between the pressure atpoint a and c, ΔP_(ac) and it is labeled net pressure loss in FIG. 10B.If the loss mechanisms are too high in a sampling device, the user mustbreathe more forcefully and perhaps more rapidly than would otherwise berequired. Too high a respiratory burden triggers an uncomfortable senseof not getting sufficient oxygen to sustain the level of metaboliceffort. For comfortable use, the respiratory burden through the wholemeasurement system should be less than ˜2″ H₂O. For a metabolic devicethat is designed to work in many conditions, from resting (peak flowrates of 15 L/min) to high-intensity exercise, such as running (peakflow rates of ˜400 L/min), care should be taken to ensure that theburden is not too high. This contradicts with the goal of pressuregenerated collection, where larger pressure drops send more gas into themixing chamber.

The pressure loss and velocity fields of a flow as it passes throughvarious geometries are well-studied. For instance, laminar pressure headloss at low Reynolds number is ∝{dot over (V)} and pressure loss due toturbulent flow is ∝{dot over (V)}². Many systems contain somecombination of the two effects, which are represented by the dischargecoefficient and pressure recovery. FIG. 11 shows the pressure recoveryin a straight wall diffuser as a function of the expansion angle. FIG.12 shows several different diffuser flow regimes, catalogued by theappearance of eddies in the stream. The different eddy formations areresponsible the changing pressure recovery shown in FIG. 11. A subset ofthe flow regimes is defined by the diffuser geometry in FIG. 13. All ofthese data are combined to intuitively understand how to construct aproportional sampling device. With increasing diffuser angles, more flowseparates from the wall to produce back pressure and irrecoverablepressure/energy loss. Using the pressure loss coefficient for a diffuserin FIG. 11 as a reference, a gentle expansion at 9-10 degrees shouldwork as an efficient diffuser for poor pressure recovery, the extremeangle of 90 degrees, or an orifice plate, would create total flowseparation as is seen in FIG. 10.

For compression, the flow tube or nozzle also should not contain a largedissipation since it will contribute to inhale pressure burden. For anozzle, the discharge coefficient has been measured to be very nearunity and nearly independent of angle or shape, as shown in FIG. 14.

A venturi tube is a geometry that contains both a nozzle to compress thegas and a diffuser to expand it. FIGS. 3A and 3B show examples ofventuri tubes with approximately 90-degree bends. In a flow diode, flowin the ab (exhale) direction should have a different characteristic thanflow in ba (inhale) direction. Specifically, when gas flows from b to a,the pressure recovery should be strongly suppressed. While flow in theab direction, recovery is encouraged. The diffuser angle for flow in theba direction should be either large or very shallow as in FIG. 11. Largewas selected for usability and length. For the exhale flow, thepermanent pressure drops for the nozzle direction, ab, will be modest asnozzles have a very mild effect on permanent pressure losses.

FIG. 15 shows the pressure recovery as a function of β, where β is theratio of the minimum tube diameter to its maximum for an orifice plate.This is the extreme case diffuser, with an equivalent to 90-degreeangle. An orifice opening creates a jet flow pattern, FIG. 12. For smallβ, less than 10% of the minimum pressure is recovered. As β increases,so does the pressure recovery, causing a reduction in respiratoryburden. Conceptually, this shows that for small β a straight venturitube with a very sharp nozzle entrance and a gradual diffuser exit canwork as an effective fluid dynamic flow diode. FIG. 16 shows one suchdesign where the diffuser and nozzle angles are chosen to produce adiode flow effect. The fact that this effect can be found in manydifferent geometries indicates that the chosen bent venturi is just oneof many possible designs.

For a general flow diode design, location of ports a and b (e.g., FIG.10) can be tuned for a more effective pressure cancelation, withpossible side effect of a reduction in driving pressure during exhale.As the flow impedance decreases, causing a drop in the gas drivingpressure, the locations of ports a and b should be located moreprecisely and likely closer together, which could decrease thecollection percent during exhale. For low exhale volumetric flow ratesassociated with resting or walking conditions, breathing through a highimpedance breathing tube is not arduous, but as activity level increasesand more air is needed by the subject, a less restrictive system isrequired (larger β for the orifice example).

This becomes a problem when respiratory burden is considered. For lowflow rates associated with resting or walking conditions, pushing airthrough a small tube is not arduous, but as activity level increases,the minimum diameter of the device should also increase. The totalpressure head loss for this device is calculated by taking thedifference between the starting pressure at the mouth interface and theending pressure where the exhaled breath rejoins the ambientenvironment. In particular, a small constriction is impractical forcomfortable use in an exercise setting, as shown in FIG. 17. For thisparticular flow tube, the comfortable respiratory burden is exceeded ata nominal flow rate of about 100 L/min. A balance between reducing orminimizing respiratory burden for the user and increasing or maximizingthe driving pressure (P_(B)−P_(A)) to deliver exhaled gas to the mixingchamber should be specifically designed to span the anticipatedphysiological range.

Possibilities for expanding the physiological range for this type ofdevice include: creating many different flow tubes (calibrated tospecific individuals or physiological ranges), moving the pressure portto idealized locations for different uses (accept the trade of lowcollection rate for efficient diode behavior), or adding additionalstructure to the flow tube to change the pressure recovery diagram (aswas done by adding the 90 degree turn to the venturi structure). Each ofthese solutions has drawbacks: producing many flow tubes, e.g., one forresting, walking, jogging, running, small people, large people, male,female, and so on becomes cumbersome. Adjusting the port locations tooptimize one effect, like the diode flow effect, can affect otherproperties of the flow tube, such as increasing or maximizing the gascollection percentage. Often the design parameters oppose each other, soachieving the minimum inhale pressure differential comes at a costimposed on the gas collection rate. So, while better pressure matchingmay be produced for the inhale, less driving pressure is developed onexhale. This slows down the collection of gas into the mixing chamber,increasing the time scale for measurement and reducing the achievabletemporal resolution of changes in physiology. Optimizing the interiorgeometry makes the design more complicated, involves additionalengineering resources, and increases the difficulty of analyticcalculation.

One possible improvement to an orifice plate or venturi design isexplored. This is to combine different flow processes; place a 90-degreeturn along the path of a standard venturi, as shown in FIGS. 3A and 3B.In this design, the flow tube bent intersects the inhale diffuser,drastically changing the inhale pressure recovery. However, as is shownin FIG. 14, the curvature of the nozzle has little effect on thepressure drop for flow in that direction. The flow through a curvednozzle and curved diffuser are examined, starting with the exhale flowdirection. As gas is pushed out of the individual and into the flow tubeit is compressed through a nozzle while going around a corner. In thissituation, the pressure change is mainly due to the idealized BernoulliEffect, where pressure is converted into kinetic energy, with littleinfluence from the nozzle. This is due to a nozzle's efficiency'srelative indifference to flow conditions.

For gas flow in the opposite direction, the gas is expanded around thecurve, rather than contracted. Curved diffusers still have the standardBernoulli pressure change moving out of the vena contracta, but diffuserpressure recovery has been shown to be sensitive to area ratios,divergence angles, and profile turning angles. These different effectshave been shown to alter the flow rates for switching between thedifferent flow profiles shown in FIG. 12 and help drive the pressuredifference between P_(C) and P_(A) toward zero during an inhale. For abend angle of 90 degrees, a diffuser angle of 10 degrees or larger mayproduce a fully developed stall and have very poor recovery. Therefore,even for low impedance devices, or flow tubes designed for exercise, theinhale recovery may be very modest and the difference between P_(C) andP_(A) will be small.

Integrating a bend (e.g., of 75-105 degrees) into the front end of theflow tube is just one enhancing geometric effect that could be used, andthe only one explored. With this design, a range of flow rates from 5L/min to 400 L/min can be spanned with 2 flow tubes, while keeping therespiratory burden under 2″ of water on exhale. Since exhaling involvesless muscle effort than inhaling, these auxiliary inhale valves helpbalance the inhale/exhale effort and make the tube easier to breathethrough, without affecting collection of the breath during exhale.Additionally, the inhale breath flow rate is not used in metabolicanalysis, so no inhale data needs to be collected. For the aerosolapplication, exhale valves could be incorporated, while not affectingthe medicine delivery.

Designing the pressure between P_(A) and P_(C) to equal zero over thewhole flow range is extremely sensitive, so additional measures aretaken to mitigate the collection of gas upon an inhale. Since b islocated at the vena contracta, which is theoretically the lowestpressure position in the system, independent of flow direction, gas flowinto the mixing chamber should always travel from P_(C) to P_(A), andnot in the opposite direction. A result of this one-way flow is theangle of the gas connections to P_(A) and P_(C) can be aligned with theexhale breath streamlines and counter aligned to the inhale flowdirection. FIG. 18 shows this diagrammatically. As shown in theschematic, during an exhale the gas entering the main stream flow fromthe collection volume has the same flow direction. Therefore, the twoshould mix with little obstruction. However, during inhale (FIG. 18B),the flow direction through the sample chamber is opposite the inhaleflow direction. The opposing flow creates an eddy that discouragesfurther flow in that direction, similar to a Tesla valve, shown in FIG.18C. Therefore, the angles of these ports deter gas flow, increasing theefficacy of the flow diode. With an effective flow diode, one-half ofthe passive gas-sampling problem—avoiding passive sample dilution—issolved, leaving the proportional gas sampling unresolved. Proportionalgas sampling is shown mathematically by:

$\begin{matrix}{\frac{{\overset{.}{V}}_{main}}{{\overset{.}{V}}_{Collection}} = {constant}} & {{Equation}\mspace{14mu} 4}\end{matrix}$

The main flow through the venturi constriction on exhale has thepressure relation shown in Equation 2. Equation 5 is the functional fitflow data shown in FIG. 17.

ΔP _(ac) ˜a{dot over (V)} _(MF) ² +b{dot over (V)} _(MF).  Equation 5

The linear term here represents the lost energy due to laminar lossesand the square term is a combination of turbulent losses and the Venturipressure effects. This same pressure difference appearing in thisequation is used to drive the flow through the ports a and c into themixing chamber. Flow through the conduit and into the mixing chamber hasa pressure relationship of Equation 6:

ΔP _(ac) ˜a′{dot over (V)} _(MC) ² +b′{dot over (V)} _(MC).  Equation 6

where once again, a′ is a measure of the permanent pressure loss due toturbulence and b′ is a measure of the laminar flow losses. For the sidestream flow, there are no Venturi effects since the input and outputports have the same cross section, therefore all of the pressure changesare due to losses. Since the pressure drops in equations 5 and 6 are thesame,

$\frac{{\overset{.}{V}}_{MC}}{{\overset{.}{V}}_{MF}} = \gamma$

is only true when a=γ² a′ and b=γb′ or approximately true when a>>b anda′>>b′ or a<<b and a′<<b′. In the special cases of dominant linear orquadratic terms, the volumetric flow ratio simplifies to a simple ratioof either laminar or turbulent. Generally speaking, γ is less than onefor our application which implies that the laminar component of the lossfor the mixing chamber flow should be relatively larger than for themain flow path. Therefore, the side stream connections should be longerand narrower to maintain proportionality.

FIG. 19 shows the measured mixing chamber collection ratio for bothinhale and exhale for the low flow version of the flow tube and FIG. 20shows the same information for the high flow. In this figure, the y-axisis the collection percent and the x-axis shows the mean flow rate pushedthrough the main flow tube path.

As a further demonstration of the efficacy of this design, FIG. 21 showsthe pressure ΔP_(ab) for several breathing cycles as a function of time.The exhale is clearly distinguished from the inhale by the largepressure changes seen on exhale and small pressure differences oninhale.

The relationship between {dot over (V)}_(MC) and {dot over (V)}_(MF) canbe used to simplify the measurement of {dot over (V)}_(MF). Typicalmetabolic devices decouple the gas collection and flow measurement intotwo separate measurements. The proportional sampling technique describedhere allows these two processes to be conducted on the same gas flow.Since ΔP_(ac) describes both the collection pressure drop and the mainflow through the flow tube, one measurement describes both flow ratessimultaneously. This enables the auxiliary chamber pressure dropmeasurement to be used as the flow measurement for the flow tube. Thisinnovation has three distinct advantages: 1. There are fewer connectionsbetween the flow tube and the mixing chamber as the gas transport andflow are measured concurrently. 2. The measurement pressure ΔP_(ac) ismeasured in the mixing chamber, at the end of a long narrow conduit.Measuring pressure differential of a laminar flow is much more stableand has fewer pressure and velocity fluctuations. This increases thefidelity of the pressure measurement and allows it to be made in thecontrolled mixing chamber environment. 3. The pressure measurement ismade in a tube where there is regular gas flow. Gas flow through thepressure measurement ports decreases the likelihood of water or salivacapillary condensing in the measurement port.

6 BREATH DYNAMICS

A deconstruction of a breath cycle is shown in FIG. 6. Therepresentative breathing cycles show the dynamic gas measurements (% CO₂and % O₂) with the bottom and middle curves and the flow ratemeasurement in the upper portion of the plot. For convenience ofdescription, the breath cycle shown in FIG. 4 is broken up into threedistinct components; inhale, dead space exhale, and alveolar exhalebreath phase. The left and right axes divide the plot into two sections:the left describes the gas concentration change and the right displaysthe changing volumetric flow rates. The bottom axis is a shared time forboth sets of curves.

The inhale, dead space, and alveolar components have different dynamicrelationships between the gas concentration and the flow rate. Two ofthem are simple because of a constant gas concentration. For inhale, thegas concentration is equal to the ambient environment (nominally 20.94%O₂ and 0.04% CO₂ for dry air with the concentrations reduced to accountfor non-zero relative humidity) flowing into the individual at inhale.Since the gas concentration is constant over the inhale (with thepossible exception of a small amount of residual end-tidal alveolar gasleft in the flow tube from the previous exhale breath), an integral ofthe flow rate determines the tidal volume, VO₂, VCO₂, and VH₂O. Themajority of the exhale varies in both gas concentration and flow rate.The exhale can be broken into two components: the dead space (the volumeof inhaled air in the mouth and esophagus that does not participate ingaseous exchange with the lungs) and the alveolar gas, the former has anearly constant gas concentration (apart from changes in humidity) andthe latter in which both the gas concentrations and flow rate vary withtime.

The dead space portion is the first part of the exhale to emerge fromthe individual and it contains the gas stored in the mouth, esophagus,and metabolic measuring device. The gas concentrations in this sectionof breath have a change in gas humidity from the subject, but the dryconcentration changes in the dead space are much smaller than thealveolar portion of the breath. The dead space breath typically resultsin the highest volumetric flow rates as the lungs are contractingrapidly from full expansion. The dead space air is either at atmosphericgas concentrations or a humidified version of ambient condition, sinceit did not enter the lungs for alveolar exchange. The second phase ofthe exhale begins, without pause, following the dead space gas. This isthe most complicated portion of the breath to measure as it has both avariable flow rate and variable constituent gas concentrations.

In comparison to the inhale, where a single measurement of ambient gasconcentration and a measurement of the volume flow rate characterizesthe entire inhale, the exhale is dynamic, and includes changes to boththe gas concentration and flow rate. Therefore, to compute relevantmetabolic measures both flow rate and concentration change have to beknown and are functions of time. Knowledge of the full temporalrelationship for flow rate and gas concentration is used to calculatethe integral of their product. The synchronization and balance of flowand gas concentration measurements is the reason why metabolic cartscollect whole breaths in a mixing chamber. When the whole breath iscollected, the gas contained in the whole breath is naturally volumeaveraged before being extracted by the gas sensors. With an averagedsample, the volume integrals can be calculated with standard flowintegrals to produce the metabolic variables. Breath-by-breathmeasurement systems don't average the data and need to havetime-synchronized high-rate measurements of both the volumetric flow andthe associated gas concentrations to directly calculate and measure themetabolic quantities.

FIGS. 7A and 7B shows the differential volume elements from the breathsin FIG. 6. FIGS. 7A and 7B differentiate between two different samplingmethods, one that has a constant volumetric pumping rate (FIG. 7A) andthe one which varies the volumetric pumping rate in proportion to theexhale flow rate (FIG. 7B). The differential volume elements of FIGS. 7Aand 7B are separated into smaller components, indicating the volumefractions of O₂, CO₂, or inert (largely N₂) gas. The total volume andfractional gas volumes for these data are integrated and summarized inTable 1 (below).

These example data show the distinction between proportional sampling ofthe exhaled breath versus a constant-rate sampling technique, as wouldoccur with a system without feedback. For this experiment, the pump ratefor the constant-rate sampling system is 50 cc/min and the proportionalpumping system removes 2% of gas from each breath relative to the flowrate. Summing the three differential volume elements together over thewhole breath delivers the tidal volume and summing specific componentswill give the gas volumes.

For the constant-rate pumped system, each bar represents a differentialvolume element in the plot of FIG. 7A. Each bar in FIG. 7A is the samesince the volume elements are being collected at a constant rateregardless of the exhale flow rate. In contrast, the volume bars for theproportional system track the shape of the exhale flow rate (FIG. 7B).FIGS. 7A and 7B show that the continuous pumping method gives a higherthan deserved weight to the volumetric gas measurements corresponding tothe parts of the respiration cycle where the flow is slower and lessweight than deserved to the volumetric gas concentrations in the regionsof the breath where the flow is more rapid. The inhaled and exhaledvolumes are assumed to be known precisely, so no Haldane or other volumecorrection factors are applied and the differences between the twocollection systems are due to the measurement bias introduced by aconstant-rate sampling pump.

Total Volume VO₂ VCO₂ O₂ % CO₂ % EE Whole Breath 1 2.14 L 0.13 L 0.10 L6.11% 4.57% 1.59 Whole Breath 2 2.23 L 0.14 L 0.10 L 6.25% 4.68% 1.69Constant Rate 1 32.8 cc 2.06 cc 1.55 cc 6.58% 4.93% 1.71 Constant Rate 234.4 cc 2.16 cc 1.62 cc 6.28% 4.73% 1.70 Proportional 1 17.1 cc 1.05 cc0.78 cc 6.11% 4.57% 1.59 Proportional 2 17.8 cc 1.11 cc 0.84 cc 6.25%4.68% 1.69

The first two rows of data in Table 1 are equivalent to a Douglas bagmeasurement where the whole breath volume is captured. These rowsrepresent a ground truth against which to compare the constant-rate andproportional sampling measurement techniques. The total volume column ofthe table shows the advantage of side-stream sampling techniques overthe traditional systems. The side-stream systems collect only a fractionof the gas relative the Douglas bag technique. The volumes of the twoside stream techniques are not equivalent in this experiment, but thepump rates and collection percent were arbitrarily chosen and could bescaled up or down to match.

Table 1 displays a fundamental difference between the exhale collectionby a proportionally pumped system compared to a constant-rate pumpsystem. With a constant pump rate, the dynamic relationship of the gasconcentration with respect to the exhale flow rate is lost and themeasured concentrations of O₂ and CO₂ become biased. For the constantflow rate, the collected volume element of end tidal gas has the samesize as the volume element from the initial dead space despite theirdifferent instantaneous exhale flow rates leading to a measuredconcentration of 6.58 and 6.28 for O₂ and 4.93 and 4.73 for CO₂, ratherthan the exhaled 6.11, 6.25, 4.57, and 4.68 gas percentages. The errorin energy expenditure (EE) calculated scales directly with the gaspercentage error and is inconsistent between the different breaths. Inthe first breath the constant rate sampling produces nearly a 10% error,while in the second breath the error is hardly present at all. In theproportional system, the gas concentration percentages are preservedsince the differential volume elements scale directly with the flowrate. Not scaling the gas collection will not only give incorrectanswers for single breaths, it will also skew the intrabreath VO₂ andVCO₂ concentrations, as is shown in Table 1.

Further, if consecutive breaths have different tidal volumes, but thesame respiration rate, a constantly pumped system may average the twobreaths as equals when in reality the physiological effects of theconsecutive breaths could be quite different.

This error introduced by constant-rate sampling varies acrossindividuals, situation, or experiment. For the case of a large, long,slow breath, a constant pumping rate may spend a relatively long timepumping the low flow rate end of the breath compared to the high flowrate beginning of a breath. The resulting breath sample will may produceaverage concentration values skewed towards the end tidal measurements,rather than a realistic balance of dead space and end tidal. However, ifa test individual has shorter breaths, with a more consistent flow rate,this systematic error in the data could disappear altogether.

FIG. 6 shows two breath exhale cycles and identifies the epochscomprising a typical breath cycle as well as the parameters of interest.For metabolic measurements, these parameters include O₂ percentage, CO₂percentage, and gas volume. The volumetric flow rate is shown as theupper trace with scale values displayed on the right-hand axis. Thebreath shown starts in the middle of an inhale with a flow rate of about−100 L/min before the subject initiates an exhale starting at around 0.5seconds. The gas concentrations for O₂ and CO₂ are represented by theupper and lower traces, respectively. The numbers shown for gasconcentrations displayed are CO₂ produced and O₂ consumed. The breathsare broken up into four distinct time regions based on their behavior:dead space, main exhale, end tidal, and inhale.

FIGS. 7A and 7B are bar charts showing the gas collection differentialvolume elements (DVEs) for two different pumping methods. The top barchart shows the DVEs for a constant pump rate system (e.g., aconventional breath-by-breath system). The constant pump rate isindicated by the equal heights of all of the DVEs. The bottom bar charthas a pump rate that is scaled proportionally by the volume flow rate.This is indicated by the varying heights of all of the DVEs. These datawere both extracted from the breathing data shown in FIG. 6. The upperbars are the DVE of inert gas entering the mixing chamber, the middlebars are CO₂, and the lower bars are O₂. The relative contribution ofeach DVE to the end tidal volume, VO₂, and VCO₂ for each bar isrepresented by the bar height.

FIG. 8 shows the velocity fields and pressure generated for a nearlydissipation-free flow around a 90-degree bend, e.g., as in the flow tubeof FIGS. 3A and 3B. The radial vectors R and X are shown by the arrowsextending diagonally from lower right to upper left. The vector R goesto the outer most area of the fluid flow and the vector X ranges throughthe flow zone. The relative pressure differences are shown in the legendwith larger pressures at the outside of the bend and smaller pressuresat the inside of the bend. The arrows in the bend show the flow velocityfield.

FIG. 9 shows the velocity fields and pressure generated for a nearlydissipation-free flow through a restriction. The relative pressuredifferences are shown in the same shading as FIG. 8, with largerpressures at the left and right ends and smaller pressures in themiddle. The arrows show the flow velocity field. There is no loss inpressure in FIG. 9, so the pressure fully recovers.

FIG. 10A shows a diagram of an orifice plate placed in a horizontalfluid flow from left to right through a conduit or lumen. The dashedlines represent the streamlines of the fluid flow. In FIG. 10A, thefluid is squeezed through a small orifice and naturally returns back toits original diameter. The curve shows the typical pressure change as afunction of distance in the horizontal direction. The pressure islargest before entering the constriction, before reaching its minimum atthe Vena contracta. The pressure recovers some of its original valuefurther down the tube. The permanent pressure losses are marked, as wellas the maximum pressure difference. The recoverable pressure change isthe difference between the pressures located at points b and c.

The bar plots above the conduit show the difference between the pressurechange for a dissipation-free system and one that includes dissipation.Both flow types start at the same pressure before reducing theirpressure immediately after the orifice. In FIG. 10A, the pressure dropsbetween points a and b are the same for both flow types, but this isn'tnecessarily the case in general. The dissipation-free system recoversall of its original pressure by the time it reaches point c, while thesystem which includes dissipation does not.

FIG. 10B is a more detailed plot of the pressure change through anorifice plate. The locations A and B from FIG. 10A are shown for thisgeometry. For flow from the left to right, a large pressure differenceis present between the two points, but for flow in the other directionthe difference in pressure between these two points is more modest.

FIG. 11 is a plot of pressure lost for a cone-shaped diffuser as afunction of the diffuser cone divergence angle. There is a minimum inpressure loss at a cone divergence angle of around 9 or 10 degrees, andthe pressure loss is greater on either side of the inflection point.

FIG. 12 shows the different levels of stall in flow through a diffuser.These flow patterns are responsible for variations in pressure recovery.

FIG. 13 is a plot of diffuser angle versus normalized length for conicaldiffusers (e.g., as in the flow tube of FIGS. 3A and 3B) andtwo-dimensional diffusers. Appreciable stall occurs at upper right, andthere is no appreciable stall at lower left. Without being bound by anyparticular theory, this shows that the appearance of eddies, energyloss, and stall is a function of both the diffuser angle and the lengthof the diffuser. The goal is to produce a flow tube that has noappreciable stall for directions with good pressure recovery and toincrease or maximize the stall for flow in directions where poorpressure recovery is desired.

FIG. 14 is a plot showing the stability of the discharge coefficient fornozzles of differing geometries. As opposed to a diffuser, the nozzle isfairly insensitive to geometry (e.g., nozzle angle, bending tube, etc.)it can be used to help create biased flow patterns.

FIG. 15 is a plot showing the pressure recovery from the minimumpressure point in for flow through an orifice. Orifice flow can beconsidered flow through a hole in a wall. Without being bound by anyparticular theory, FIG. 15 shows that the pressure recovery is dependenton Beta, or the ratio of the minimum flow diameter and main flowdiameter. Since the pressure reaches a minimum, there exists a pair ofpoints for all Beta where the absolute pressure is the same for twopoints on either side of the minimum. This suggests an orifice geometrycan be used to create a perfect flow diode, independent of flow rate.This is because when two different points are in a pressure equilibriumthere is no driving force to promote flow between them. This informationcan be used to choose the chamber pick-off points (i.e., the locationsof ports P_(A) and P_(C)) in flow tubes similar to FIG. 3A, 3B, 3E, 3F,16A, or 16B.

FIGS. 16A and 16B shows SolidWorks™ simulations of the pressure andvelocity fields inside of an asymmetric constriction geometry for flowin opposite directions (down in FIG. 16A and up in FIG. 16B). Therelative pressure is the same scale for both directions and is shadedaccording to the shading bars. The arrows represent the velocity fieldvectors and in both cases flow separation, as shown in FIG. 12, is seenby circularity in the velocity. The flow direction with larger flowseparation has a poorer pressure recovery than the alternate direction,suggesting that an optimized straight device like this one could alsowork as a passive flow tube like the ones shown in FIGS. 3A-3F. For theexample, the tube shown in FIGS. 16A and 16B could be modified forpassive side stream sampling by adding gas collection side stream portsat the top of the narrow neck and the bottom of the tube, labeled P_(A)and P_(C) in the drawing.

FIG. 17 is a plot of the measured gas flow rate as a function ofpressure differential across the flow tube for a generic sensor. Thisdata is extracted from a low-flow, or resting, sensor since just 100L/min produces a pressure drop of 2″/H₂O. The relationship between flowinduced pressure change and flow rate is quadratic, independent of itssource (dissipative or not). The flow rate entering the mixing chamberof FIG. 5B will have a functionally comparable pressure drop as the datain FIG. 17, but the flow rates should be reduced by roughly a factor of50. The proportionality of the flow rate into the mixing chamber to theflow rate through the flow tube implies that a differential pressuremeasurement can also be made at the point where the sample and returntubes enter and exit the mixing chamber, thereby eliminating the needfor additional pressure tubes attached to the flow tube. In other words,measurement of the flow into and out of the mixing chamber can be usedas a proxy measurement of flow through the flow tube.

FIGS. 18A and 18B shows a secondary method of reducing the amount offlow into the auxiliary chamber when the flow tube is used as acollection device. When the flow tube is used for extraction the sameprinciples hold, but inhale and exhale are reversed. The main gas flowis indicated by large arrows and the flow into and out of the collectionchamber is indicated by smaller arrows. When the velocity vectors ofboth fields are lined up at the entrance and exit ports, fluid is freeto flow into the collection chamber. But when the flow vectors of thetwo different flow paths are in opposition, additional flow stagnationis encountered and flow along the auxiliary path is further suppressed.

FIG. 18C shows a design for a Tesla flow diode which uses the principleillustrated in FIGS. 18A and 18B to create mono-directional flow. In theTesla diode, the reverse direction flow is created by the fluidspreference to follow the wall contour of its conduit. But theconflicting flow direction principle is the same.

FIG. 19 is a plot showing the effectiveness of the proportional samplingtechnique for three different high-flow flow tubes like the one in FIGS.3A and 3B. The data were collected over a wide variety of tidal volumesand average flowrates. The x-axis is the mean flow rate over the courseof a single breath. Negative flow rates represent inhale flow andpositive flow rates are for exhale flows. The y-axis is the ratio of theamount of gas collected in the mixing chamber to the amount of gas thatpasses through the flow tube, divided by 100. A value of 100% on they-axis indicates that all of the exhale traveled into the mixingchamber, which is the standard for metabolic carts. For an ideal passiveside-stream sampling system, the collection percent for exhale is aconstant number representing an exact proportional sampling and theinhale collection is zero.

FIG. 20 shows the same data set as FIG. 19, but for a flow tube like theone in FIGS. 3A and 3B with a higher respiratory burden. The gain withthe higher burden is an increase in the collection percent from about0.8% to 2%, allowing the collection chamber to fill more rapidly withexhaled breath during use.

FIG. 21 shows the raw data used to estimate or determine the volume ofexhale/inhale entering the collection chamber in the passive side streamsampling system of FIG. 5B. The x-axis is time in seconds and the y-axisis the differential pressure between ports PA and PC from FIGS. 3A and3B. Larger differential pressures represent larger flow rates of gasentering the mixing chamber as in FIG. 17.

FIG. 21 shows that the flow rate of gas entering the chamber varies overmany breathing cycles, starting from rapid flow at the beginning toslower flow by the end. The raw data shown here displays the differencein pressures generated in the two flow directions. Each cycle has aninhale and an exhale. For this device, each inhale has a negativedifferential pressure and the exhale is positive.

FIG. 22 is a close-up of a few breathing cycles from FIG. 21. When thetime axis is expanded, it is much easier to see the difference betweenan inhale and an exhale. The horizontal and vertical axes show time inseconds and differential pressure in Pa, respectively.

FIG. 23A is a cross-sectional view of a mixing chamber 2312 with aperforated baffle 2326 and a perforated circuit board or panel 2322disposed therein. FIG. 23B is a top, cut-away view of the mixing chamber2312 and perforated circuit board 2322 shown in FIG. 23A. The perforatedbaffle 2326 and perforated circuit board 2322 provide a low resistancepath for gas flow and aid in mixing the expired boluses of gas beforesame arrive at gas sensor(s) 2320 (e.g., oxygen and/or carbon dioxidesensors). Put differently, the perforations in the perforated baffle2326 and perforated circuit board 2322 foster mixing of multiple breathfractions. This or a similar arrangement provides a low resistance pathfor gas flow while ensuring each incoming breath mixes with the residualfrom previous breaths, forming a volumetric average with the previousfew exhaled breaths.

7 CONCLUSION

In conclusion, a compact accurate metabolic device with the samefidelity of larger metabolic carts is disclosed. It can passivelycollect exhaled breath at a collection rate that is directlyproportional to the exhale flow rate to produce a control volume of gaswith exactly the same volume concentration percentages as a Douglas bagcollection of the entire breath. The values of VO₂, VCO₂, and minuteventilation can be used to calculate energy expenditure and respiratoryexchange ratio, among other variables, in a package that is portable andunobtrusive to the user. In particular, because the flow tube ispassive—it has no moving parts or electronics—it can be disconnectedfrom the mixing chamber and sanitized between uses by soaking indisinfectant. The lack of moving parts also reduces manufacturing costand increases service life. This system alleviates the requirement offast sensors and complicated calibration procedures common to mobilebreath-by breath systems, enabling for a low-cost, personal-use sensor.It can make on-demand measurements of respiratory exchange ratio, VO₂,tidal volume, minute volume energy expenditure, and other metricsrelated to metabolic health and performance with supporting systemsoftware.

While various inventive embodiments have been described and illustratedherein, those of ordinary skill in the art will readily envision avariety of other means and/or structures for performing the functionand/or obtaining the results and/or one or more of the advantagesdescribed herein, and each of such variations and/or modifications isdeemed to be within the scope of the inventive embodiments describedherein. More generally, those skilled in the art will readily appreciatethat all parameters, dimensions, materials, and configurations describedherein are meant to be exemplary and that the actual parameters,dimensions, materials, and/or configurations will depend upon thespecific application or applications for which the inventive teachingsis/are used. Those skilled in the art will recognize or be able toascertain, using no more than routine experimentation, many equivalentsto the specific inventive embodiments described herein. It is,therefore, to be understood that the foregoing embodiments are presentedby way of example only and that, within the scope of the appended claimsand equivalents thereto, inventive embodiments may be practicedotherwise than as specifically described and claimed. Inventiveembodiments of the present disclosure are directed to each individualfeature, system, article, material, kit, and/or method described herein.In addition, any combination of two or more such features, systems,articles, materials, kits, and/or methods, if such features, systems,articles, materials, kits, and/or methods are not mutually inconsistent,is included within the inventive scope of the present disclosure.

Also, various inventive concepts may be embodied as one or more methods,of which an example has been provided. The acts performed as part of themethod may be ordered in any suitable way. Accordingly, embodiments maybe constructed in which acts are performed in an order different thanillustrated, which may include performing some acts simultaneously, eventhough shown as sequential acts in illustrative embodiments.

All definitions, as defined and used herein, should be understood tocontrol over dictionary definitions, definitions in documentsincorporated by reference, and/or ordinary meanings of the definedterms.

The indefinite articles “a” and “an,” as used herein in thespecification and in the claims, unless clearly indicated to thecontrary, should be understood to mean “at least one.”

The phrase “and/or,” as used herein in the specification and in theclaims, should be understood to mean “either or both” of the elements soconjoined, i.e., elements that are conjunctively present in some casesand disjunctively present in other cases. Multiple elements listed with“and/or” should be construed in the same fashion, i.e., “one or more” ofthe elements so conjoined. Other elements may optionally be presentother than the elements specifically identified by the “and/or” clause,whether related or unrelated to those elements specifically identified.Thus, as a non-limiting example, a reference to “A and/or B”, when usedin conjunction with open-ended language such as “comprising” can refer,in one embodiment, to A only (optionally including elements other thanB); in another embodiment, to B only (optionally including elementsother than A); in yet another embodiment, to both A and B (optionallyincluding other elements); etc.

As used herein in the specification and in the claims, “or” should beunderstood to have the same meaning as “and/or” as defined above. Forexample, when separating items in a list, “or” or “and/or” shall beinterpreted as being inclusive, i.e., the inclusion of at least one, butalso including more than one, of a number or list of elements, and,optionally, additional unlisted items. Only terms clearly indicated tothe contrary, such as “only one of” or “exactly one of,” or, when usedin the claims, “consisting of,” will refer to the inclusion of exactlyone element of a number or list of elements. In general, the term “or”as used herein shall only be interpreted as indicating exclusivealternatives (i.e. “one or the other but not both”) when preceded byterms of exclusivity, such as “either,” “one of,” “only one of,” or“exactly one of.” “Consisting essentially of,” when used in the claims,shall have its ordinary meaning as used in the field of patent law.

As used herein in the specification and in the claims, the phrase “atleast one,” in reference to a list of one or more elements, should beunderstood to mean at least one element selected from any one or more ofthe elements in the list of elements, but not necessarily including atleast one of each and every element specifically listed within the listof elements and not excluding any combinations of elements in the listof elements. This definition also allows that elements may optionally bepresent other than the elements specifically identified within the listof elements to which the phrase “at least one” refers, whether relatedor unrelated to those elements specifically identified. Thus, as anon-limiting example, “at least one of A and B” (or, equivalently, “atleast one of A or B,” or, equivalently “at least one of A and/or B”) canrefer, in one embodiment, to at least one, optionally including morethan one, A, with no B present (and optionally including elements otherthan B); in another embodiment, to at least one, optionally includingmore than one, B, with no A present (and optionally including elementsother than A); in yet another embodiment, to at least one, optionallyincluding more than one, A, and at least one, optionally including morethan one, B (and optionally including other elements); etc.

In the claims, as well as in the specification above, all transitionalphrases such as “comprising,” “including,” “carrying,” “having,”“containing,” “involving,” “holding,” “composed of,” and the like are tobe understood to be open-ended, i.e., to mean including but not limitedto. Only the transitional phrases “consisting of” and “consistingessentially of” shall be closed or semi-closed transitional phrases,respectively, as set forth in the United States Patent Office Manual ofPatent Examining Procedures, Section 2111.03.

1. A flow-rate proportional passive side-stream sampling systemcomprising: a bent flow tube to receive an exhaled breath from a person;a mixing chamber, in fluid communication with a first port between aninlet of the bent flow tube and an outlet of the bent flow tube, toreceive a fraction of the exhaled breath collected in proportion to aninstantaneous flow rate of the exhaled breath; and at least one sensor,in fluid communication with gas in the mixing chamber, to measure atleast one of a volumetric flow rate, an oxygen content, a carbon dioxidecontent, an oxygen partial pressure, or a carbon dioxide partialpressure of the fraction of the exhaled breath.
 2. The flow-rateproportional passive side-stream sampling system of claim 1, wherein thebent flow tube has a curve of about 75 degrees to about 105 degreesbetween the inlet and the outlet, the bent flow tube defining an innerlumen extending from the proximal end to the distal end to convey theexhaled breath from the proximal end to the distal end, the first portbeing disposed between the bend and the outlet.
 3. The flow-rateproportional passive side-stream sampling system of claim 2, wherein thebent flow tube has a second port disposed between the inlet and thebend.
 4. The flow-rate proportional passive side-stream sampling systemof claim 2, further comprising: at least one valve, disposed between theinlet and the bend and in fluid communication with the inner lumen, torelieve pressure in the inner lumen during an inhalation by the person.5. The flow-rate proportional passive side-stream sampling system ofclaim 2, further comprising: a saliva trap, disposed in fluidcommunication with the inner lumen, to collect saliva excreted by theperson.
 6. The flow-rate proportional passive side-stream samplingsystem of claim 2, further comprising: a removable mouthpiece connectedto the inlet of the bent flow tube.
 7. The flow-rate proportionalpassive side stream sampling system of claim 1, wherein the mixingchamber further comprises a perforated baffle and/or a perforatedcircuit board disposed between the inlet and the at least one sensor tofoster mixing of multiple breath fractions.
 8. The flow-rateproportional passive side stream sampling system of claim 1, wherein theat least one sensor is disposed in the mixing chamber.
 9. A method ofproportional passive flow-rate sampling, the method comprising:receiving an exhaled breath from a person at an inlet of a bent flowtube; conveying a fraction of the exhaled breath from a first portbetween the inlet of the flow tube and a bend in the bent flow tube to amixing chamber, the fraction of the exhaled breath being in proportionto an instantaneous flow rate of the exhaled breath; and measuring, withat least one sensor, at least one of a volumetric flow rate, an oxygencontent, a carbon dioxide content, an oxygen partial pressure, or acarbon dioxide partial pressure of the fraction of the exhaled breath.10. The method of claim 9, wherein the bend in the bent flow tube isabout 75 degrees to about 105 degrees between the inlet and the outlet,the tube defining an inner lumen extending from the proximal end to thedistal end to convey the exhaled breath from the proximal end to thedistal end, the first port being disposed between the bend and theoutlet.
 11. The method of claim 9, wherein the bent flow tube has asecond port disposed between the bend and the outlet, and furthercomprising: conveying gas from the mixing chamber to the second part;and emitting the gas via the outlet.
 12. The method of claim 9, furthercomprising: actuating at least one valve, disposed between the inlet andthe bend in the bent flow tube, to relieve pressure in the inner lumenduring an inhalation by the person.
 13. The method of claim 9, furthercomprising: collecting saliva excreted by the person with a saliva trap.14. The method of claim 9, further comprising: mixing fractions ofmultiple exhaled breaths in the mixing chamber.
 15. A flow tube for ametabolic cart, the flow tube comprising: a proximal end to receive anexhalation from a person; a distal end; a bend between the proximal endand the distal end; a first port between the proximal end and the bend;and a second port between the bend and the distal end to convey aportion of the exhalation to a mixing chamber in fluid communicationwith a lumen extending from the proximal end to the distal end to conveythe exhalation from the proximal end to the distal end,
 16. The flowtube of claim 15, wherein the bend is about 75 degrees to about 105degrees.
 17. The flow tube of claim 15, wherein the bend is about 90degrees.
 18. The flow tube of claim 15, further comprising: at least onevalve, disposed between the proximal end and the bend and in fluidcommunication with the lumen, to relieve pressure in the lumen during aninhalation by the person.
 19. The flow tube of claim 15, furthercomprising: a saliva trap, disposed in fluid communication with thelumen, to trap saliva excreted by the person.
 20. The flow tube of claim15, further comprising: a removable mouthpiece inserted into theproximal end.